An offset printing system having two plate cylinders which can be associated with a blanket cylinder has previously been proposed. The plate cylinders can be horizontally disengaged from the blanket cylinder. If each of the plate cylinders includes adjustment systems, for example to correct copying of printing errors, deviations upon bending, or clamping of the printing plates, and adjustment arrangements for lateral, circumferential and diagonal register, it becomes difficult to shift the plate cylinders while maintaining register for further printing. The system, further, is very complex, as illustrated in the publication describing the system, German Utility Model DE-GM 84 10 619. The system further requires separate disengagement systems in order to counteract damage if, possibly, the web might tear.